On the reproduction of closed-loop experimental data by an LFT perturbed model set

This paper investigates the consistency between frequency domain closed-loop experimental data and a model set with linear fractional unstructured uncertainties. When the number of unstable poles of the transfer function matrices (TFM) in the model set are identical, a necessary and sufficient condition is derived for the reproduction of experimental data. This condition is expressed as the non-positiveness of a quadratic form of the external disturbances and measurement errors, together with a linear constraint. In this derivation, it is not required that all the TFMs in the model set are internally stabilizable by the controller. The condition is also not necessary for the closed-loop system consisting of the nominal model and the controller to be internally stable. It is believed that this condition is theoretically and computationally attractive in model set validation, no matter whether a deterministic or stochastic framework is adopted.